accurate {aTSA} R Documentation

## Accurate Computation

### Description

Computes the accurate criterion of smoothed (fitted) values.

### Usage

```accurate(x, x.hat, k, output = TRUE)
```

### Arguments

 `x` a numeric vector of original values. `x.hat` a numeric vector of smoothed (fitted) values. `k` the number of parameters in obtaining the smoothed (fitted) values. `output` a logical value indicating to print the results in R console. The default is `TRUE`.

### Details

See http://www.dms.umontreal.ca/~duchesne/chap12.pdf in page 616 - 617 for the details of calculations for each criterion.

### Value

A vector containing the following components:

 `SST` the total sum of squares. `SSE` the sum of the squared residuals. `MSE` the mean squared error. `RMSE` the root mean square error. `MAPE` the mean absolute percent error. `MPE` the mean percent error. `MAE` the mean absolute error. `ME` the mean error. `R.squared` R^2 = 1 - SSE/SST. `R.adj.squared` the adjusted R^2. `RW.R.squared` the random walk R^2. `AIC` the Akaike's information criterion. `SBC` the Schwarz's Bayesian criterion. `APC` the Amemiya's prediction criterion

### Note

If the model fits the series badly, the model error sum of squares `SSE` may be larger than `SST` and the `R.squared` or `RW.R.squared` statistics will be negative. The `RW.R.squared` uses the random walk model for the purpose of comparison.

Debin Qiu

### Examples

```X <- matrix(rnorm(200),100,2)
y <- 0.1*X[,1] + 2*X[,2] + rnorm(100)
y.hat <- fitted(lm(y ~ X))
accurate(y,y.hat,2)
```

[Package aTSA version 3.1.2 Index]